| 无限的可解SD_2－群（Ⅱ）──有限剩余情形 |
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| 引用本文： | 刘合国. 无限的可解SD_2－群（Ⅱ）──有限剩余情形[J]. 数学学报, 1994, 37(6). DOI: cnki:ISSN:05831431.0.1994-06-000 |
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| 作者姓名： | 刘合国 |
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| 作者单位： | 湖北大学数学系 |
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| 摘 要： | 如果对多重循环群Ｇ的每个有限剩余的真子群都是可以由二元生成的，那么我们就把Ｇ叫做ＲＤ＿２－群。在本文里，我们确定了无限的ＲＤ＿２－群的结构，证明了ＲＤ＿２－群是可以由二元生成的。这些结果推广了作者已经得到的关于无限的可解ＳＤ＿２群的全部结果，见［４］．
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| 关 键 词： | 生成元，RD_2－群，Hirsch长度 |
| 收稿时间： | 1991-11-12 |
On Solvable SD_2 -Grotip of Infinite Order |
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| Liu Heguo. On Solvable SD_2 -Grotip of Infinite Order[J]. Acta Mathematica Sinica, 1994, 37(6). DOI: cnki:ISSN:05831431.0.1994-06-000 |
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| Authors: | Liu Heguo |
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| Affiliation: | Liu Heguo(Department of Mathematics of Hubei University,Wuhan 430062, China ) |
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| Abstract: | Let G be a polycyclic group of infinite order. we show that G is 2-generated andof Hirsch length 1 or 2 if every proper subgroup of arbitrary finite quotient group of G is 2-0generated.If it is the case,moreover, G is both supersolvable and metabelian if its Hirsch lengthis1, and G(3)= 1 and G is a natural extension of by certain finite subgroup of GL(2,Z)if its Hirb,ch length is 2. |
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| Keywords: | polycyclic group Hirsch length 2generated finite residue |
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